AliMFTTrackExtrap.cxx

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/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
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 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
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 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

/* $Id$ */

//-----------------------------------------------------------------------------
// Class AliMFTTrackExtrap
// ------------------------
// Tools for track extrapolation in ALICE MFT
// Adapted from AliMUONTrackExtrap by R. Tieulent
// Original Author: Philippe Pillot
//-----------------------------------------------------------------------------

#include "AliMFTTrackExtrap.h"  
#include "AliMFTTrackParam.h"
#include "AliMFTConstants.h"

#include "AliMagF.h"
#include "AliExternalTrackParam.h"

#include <TGeoGlobalMagField.h>
#include <TGeoManager.h>
#include <TMath.h>
#include <TDatabasePDG.h>

#include <Riostream.h>

using std::endl;
using std::cout;
ClassImp(AliMFTTrackExtrap) // Class implementation in ROOT context

const Double_t AliMFTTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMFTConstants::DefaultPlaneZ(0) + AliMFTConstants::DefaultPlaneZ(9));
//const Double_t AliMFTTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
      Double_t AliMFTTrackExtrap::fgSimpleBValue = 0.;
      Bool_t   AliMFTTrackExtrap::fgFieldON = kFALSE;
const Bool_t   AliMFTTrackExtrap::fgkUseHelix = kTRUE;
const Int_t    AliMFTTrackExtrap::fgkMaxStepNumber = 5000;
const Double_t AliMFTTrackExtrap::fgkHelixStepLength = 0.1;
const Double_t AliMFTTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;

//__________________________________________________________________________
void AliMFTTrackExtrap::SetField()
{
  const Double_t x[3] = {0.,0.,fgkSimpleBPosition};
  Double_t b[3] = {0.,0.,0.};
  TGeoGlobalMagField::Instance()->Field(x,b);
  cout<<Form("Field = %e %e %e",b[0],b[1],b[2])<<endl;
  fgSimpleBValue = b[2];
  fgFieldON = (TMath::Abs(fgSimpleBValue) > 1.e-10) ? kTRUE : kFALSE;
//  fgFieldON = kFALSE;
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
{
  
//  if (bendingMomentum == 0.) return 1.e10;
//  
//  const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
//  
//  return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
}

//__________________________________________________________________________
Double_t 
AliMFTTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
{
  
//  if (impactParam == 0.) return 1.e10;
//  
//  const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
//  
//  if (fgFieldON) 
//  {
//    return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
//  }
//  else 
//  {
//    return AliMUONConstants::GetMostProbBendingMomentum();
//  }
}
//__________________________________________________________________________
Double_t AliMFTTrackExtrap::Sagitta(Int_t nVal, Double_t *xVal, Double_t *yVal, Double_t &distL2, Double_t &q2)
{
  cout<<"Sagitta"<<endl;
  Double_t q0,q1,chi2;
  // fit by a polynom of 2nd order
  chi2 = QuadraticRegression(nVal,xVal ,yVal, q0, q1,q2);
  cout<<Form("q param = %f  %f  %f  chi2 = %e ",q0, q1,q2,chi2)<<endl;
  cout<<Form("pt from 2nd order parameter %f ",0.01/q2/2.*0.3*fgSimpleBValue/10.)<<endl;
  

  Double_t maxDist = 0.;
  Int_t i1 = -1;
  Int_t i2 = -1;
  Double_t sagitta = 0.;
  Double_t dist ;
  Double_t distTot = 0.;

  for (int i=0; i<nVal-1; i++) {
    distTot += TMath::Sqrt((xVal[i]-xVal[i+1]) * (xVal[i]-xVal[i+1]) + (yVal[i]-yVal[i+1]) * (yVal[i]-yVal[i+1]));

    for (int j = i+1; j<nVal; j++) {
      Double_t dist = (xVal[i]-xVal[j]) * (xVal[i]-xVal[j]) + (yVal[i]-yVal[j]) * (yVal[i]-yVal[j]);
      if(dist>maxDist){
        i1 = i;
        i2 = j;
        maxDist = dist;
      }
    }
  }
  
  cout<<Form("distMAx = %f distTot =%f   i1 = %d i2 =%d",TMath::Sqrt(maxDist),distTot,i1,i2)<<endl;
  
  distL2 = 1.e-2*TMath::Sqrt((xVal[i1]-xVal[i2]) * (xVal[i1]-xVal[i2]) + (yVal[i1]-yVal[i2]) * (yVal[i1]-yVal[i2]) );
  
  Double_t p1 = (yVal[i1]-yVal[i2]) / (xVal[i1]-xVal[i2]);
  Double_t p0 = yVal[i2] - xVal[i2] * p1;
  cout<<Form("p param = %f  %f  ",p0, p1)<<endl;
  q2 = TMath::Sign(q2,q1*q2*(-(p0 + p1 * (xVal[i1]+xVal[i2])/2.))*(fgSimpleBValue));

  
  Double_t y12 = q0+q1*xVal[i1]+q2*xVal[i1]*xVal[i1];
  Double_t y22 = q0+q1*xVal[i2]+q2*xVal[i2]*xVal[i2];
  cout<<Form("x1, y1 %f  %f  ",xVal[i1], y12)<<endl;
  cout<<Form("x2, y2 %f  %f  ",xVal[i2], y22)<<endl;

//  Double_t p12 = (y12-y22) / (xVal[i1]-xVal[i2]);
//  Double_t p02 = y22 - xVal[i2] * p12;
//  cout<<Form("p2 param = %f  %f  ",p02, p12)<<endl;

  Double_t maxSagitta = 0.;
  for (int i=0; i<20; i++) {
    Double_t step =TMath::Abs(xVal[i1]-xVal[i2])/20.;
    Double_t xmiddle = xVal[i1] + i*step;
    
    Double_t y1 = p0 + p1 * xmiddle;
    Double_t p1perp = -1./p1;
    Double_t p0perp = p0 + xmiddle *(p1-p1perp);
    //cout<<Form("p param perp = %f  %f  ",p0perp, p1perp)<<endl;
    
    Double_t xmax = (p1perp - q1 + TMath::Sqrt(p1perp*p1perp - 2*p1perp*q1 + q1*q1 + 4*p0perp*q2 - 4*q0*q2))/(2*q2);
    Double_t xmax2 = -(q1 -p1perp + TMath::Sqrt(p1perp*p1perp - 2*p1perp*q1 + q1*q1 + 4*p0perp*q2 - 4*q0*q2))/(2*q2);
    //    cout<<Form("xmax = %f   xmax2  %f",xmax,xmax2)<<endl;
    
    if (TMath::Abs(xmax2-xmiddle) < TMath::Abs(xmax-xmiddle)) xmax = xmax2;
    
    
    Double_t y2 = q0 + q1 * xmax  + q2 * xmax * xmax;
    
    sagitta = 1e-2*TMath::Sqrt((xmiddle-xmax) * (xmiddle-xmax) + (y1-y2) * (y1-y2) );
    
    //    cout<<Form("sagitta = %f   Bz = %f",sagitta,fgSimpleBValue)<<endl;
    
    sagitta = TMath::Sign(sagitta,q1*q2*(-y1)*(fgSimpleBValue));
    
    if(TMath::Abs(sagitta)>TMath::Abs(maxSagitta)) maxSagitta = sagitta;
    
  }
  cout<<Form(" Max sagitta = %e => pt = %f",maxSagitta, 0.3*0.5*distL2*distL2/8./maxSagitta)<<endl;
//  p0 = p02;
//  p1 = p12;
//  
//
//   maxSagitta = 0.;
//  for (int i=0; i<20; i++) {
//    Double_t step =TMath::Abs(xVal[i1]-xVal[i2])/20.;
//    Double_t xmiddle = xVal[i1] + i*step;
//    
//    Double_t y1 = p0 + p1 * xmiddle;
//    Double_t p1perp = -1./p1;
//    Double_t p0perp = p0 + xmiddle *(p1-p1perp);
//    //cout<<Form("p param perp = %f  %f  ",p0perp, p1perp)<<endl;
//    
//    Double_t xmax  =  (p1perp - q1 + TMath::Sqrt(p1perp*p1perp - 2*p1perp*q1 + q1*q1 + 4*p0perp*q2 - 4*q0*q2))/(2*q2);
//    Double_t xmax2 = -(q1 - p1perp + TMath::Sqrt(p1perp*p1perp - 2*p1perp*q1 + q1*q1 + 4*p0perp*q2 - 4*q0*q2))/(2*q2);
//    
//    if (TMath::Abs(xmax2-xmiddle) < TMath::Abs(xmax-xmiddle)) xmax = xmax2;
//    
//    
//    Double_t y2 = q0 + q1 * xmax  + q2 * xmax * xmax;
//    
//    sagitta = 1e-2*TMath::Sqrt((xmiddle-xmax) * (xmiddle-xmax) + (y1-y2) * (y1-y2) );
//    
//    
//    sagitta = TMath::Sign(sagitta,q1*q2*(-y1)*(fgSimpleBValue));
//    
//    if(sagitta>maxSagitta) maxSagitta = sagitta;
//    
//  }
//  cout<<Form(" Max sagitta 2 = %e => pt = %f",maxSagitta, 0.3*0.5*distL2*distL2/8./maxSagitta )<<endl;

  return maxSagitta;
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::LinearRegression(Int_t nVal, Double_t *xVal, Double_t *yVal, Double_t &p0, Double_t &p1)
{
  Double_t meanx =0, meany=0.;

  for (Int_t i = 0; i< nVal; i++) {
    meanx =(meanx*i+xVal[i])/(i+1);
    meany =(meany*i+yVal[i])/(i+1);
  }
  Double_t cov_xy = 0., var_x=0., var_y=0.;
  for (Int_t i = 0; i< nVal; i++) {
    var_x  += (xVal[i] -meanx) * (xVal[i] -meanx);
    var_y  += (yVal[i] -meany) * (yVal[i] -meany);
    cov_xy += (xVal[i] -meanx) * (yVal[i] -meany);
  }
  if(var_x<1.e-6) return 0.;
  p1 = cov_xy/var_x;
  p0 = meany - p1 * meanx;
  
  Double_t chi2 = 0.;
  Double_t yest=0.;
  for (Int_t i = 0; i< nVal; i++) {
    yest = xVal[i]*p1+p0;
    chi2 += (yest-yVal[i]) * (yest-yVal[i]);
  }
  chi2 /= var_y;
  
  
  return chi2;
}
//__________________________________________________________________________
Double_t AliMFTTrackExtrap::QuadraticRegression(Int_t nVal, Double_t *xVal, Double_t *yVal, Double_t &p0, Double_t &p1, Double_t &p2)
{
  
  TMatrixD y(nVal,1);
  TMatrixD x(nVal,3);
  TMatrixD xtrans(3,nVal);
  
  for (int i=0; i<nVal; i++) {
    y(i,0) = yVal[i];
    x(i,0) = 1.;
    x(i,1) = xVal[i];
    x(i,2) = xVal[i]*xVal[i];
    xtrans(0,i) = 1.;
    xtrans(1,i) = xVal[i];
    xtrans(2,i) = xVal[i]*xVal[i];
  }
  TMatrixD tmp(xtrans,TMatrixD::kMult,x);
  tmp.Invert();
  
  TMatrixD tmp2(xtrans,TMatrixD::kMult,y);
  TMatrixD b(tmp,TMatrixD::kMult,tmp2);
  
  p0 = b(0,0);
  p1 = b(1,0);
  p2 = b(2,0);
  
  // chi2 = (y-xb)^t . W . (y-xb)
  TMatrixD tmp3(x,TMatrixD::kMult,b);
  TMatrixD tmp4(y,TMatrixD::kMinus,tmp3);
  TMatrixD chi2(tmp4,TMatrixD::kTransposeMult,tmp4);
  
  
  return chi2(0,0);
}
//__________________________________________________________________________
Double_t AliMFTTrackExtrap::CircleRegression(Int_t nVal, Double_t *xVal, Double_t *yVal)
{
  Double_t sumxi2 =0., sumxi =0., sumxiyi =0., sumyi =0.,sumyi2 =0., sumxi3 =0., sumyi3 =0.;
  Double_t sumxi2yi=0., sumxiyi2=0.;
  Double_t xi,yi, ri;
  for (int i=0; i<nVal; i++) {
    xi = xVal[i]/100.;
    yi = yVal[i]/100.;
    ri = TMath::Sqrt(xi*xi + yi*yi);
//    xi /= ri*ri;
//    yi /= ri*ri;

    sumxi += xi;
    sumyi += yi;
    sumxi2 += xi*xi;
    sumyi2 += yi*yi;
    sumxi3 += xi*xi*xi;
    sumyi3 += yi*yi*yi;
    sumxiyi += xi*yi;
    sumxi2yi += xi*xi*yi;
    sumxiyi2 += xi*yi*yi;
  }

  Double_t A = nVal * sumxi2 - sumxi*sumxi;
  Double_t B = nVal * sumxiyi - sumxi*sumyi;
  Double_t C = nVal * sumyi2 - sumyi*sumyi;
  Double_t D = 0.5*(nVal*sumxiyi2 -sumxi*sumyi2  +nVal*sumxi3 -sumxi*sumxi2);
  Double_t E = 0.5*(nVal*sumxi2yi -sumyi*sumxi2  +nVal*sumyi3 -sumyi*sumyi2);

  Double_t aM = (D*C-B*E) / (A*C-B*B);
  Double_t bM = (A*E-B*D) / (A*C-B*B);

  Double_t rM = 0.;
  Double_t rK = 0.;

  for (int i=0; i<nVal; i++) {
    xi = xVal[i]/100.;
    yi = yVal[i]/100.;

    rM += TMath::Sqrt( (xi-aM)*(xi-aM) + (yi-bM)*(yi-bM) );
    rK +=  ((xi-aM)*(xi-aM) + (yi-bM)*(yi-bM) );
  }
  rM /= nVal;
  rK = TMath::Sqrt(rK/nVal);

  cout<<Form("aM %f bM %f rM %f rK %f => pt = %f or %f ",aM,bM,rM,rK,rM*0.3*0.5, rK*0.3*0.5)<<endl;
  
  return (rM+rK)/2.;
}

//__________________________________________________________________________
void AliMFTTrackExtrap::LinearExtrapToZ(AliMFTTrackParam* trackParam, Double_t zEnd)
{
  
  if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
  
  // Compute track parameters
  Double_t dZ = zEnd - trackParam->GetZ();

  trackParam->SetX(trackParam->GetX() + trackParam->GetSlopeX() * dZ);
  trackParam->SetY(trackParam->GetY() + trackParam->GetSlopeY() * dZ);
  trackParam->SetZ(zEnd);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::LinearExtrapToZCov(AliMFTTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
{
  
  if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
  
  // No need to propagate the covariance matrix if it does not exist
  if (!trackParam->CovariancesExist()) {
    cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
    // Extrapolate linearly track parameters to "zEnd"
    LinearExtrapToZ(trackParam,zEnd);
    return;
  }
  
  // Compute track parameters
  Double_t dZ = zEnd - trackParam->GetZ();
  trackParam->SetX(trackParam->GetX() + trackParam->GetSlopeX() * dZ);
  trackParam->SetY(trackParam->GetY() + trackParam->GetSlopeY() * dZ);
  trackParam->SetZ(zEnd);
  
  // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
  TMatrixD jacob(5,5);
  jacob.UnitMatrix();
  jacob(0,2) = dZ;
  jacob(1,3) = dZ;
  
  // Extrapolate track parameter covariances to "zEnd"
  TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
  TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
  trackParam->SetCovariances(tmp2);
  
  // Update the propagator if required
  if (updatePropagator) trackParam->UpdatePropagator(jacob);
}

//__________________________________________________________________________
Bool_t AliMFTTrackExtrap::ExtrapToZ(AliMFTTrackParam* trackParam, Double_t zEnd)
{
//return AliMFTTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
  if (!fgFieldON) {
    AliMFTTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
    return kTRUE;
  }
  else if (fgkUseHelix) return AliMFTTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
  else return AliMFTTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
}

//__________________________________________________________________________
Bool_t AliMFTTrackExtrap::ExtrapToZHelix(AliMFTTrackParam* trackParam, Double_t zEnd)
{
//  cout<<"I-AliMFTTrackExtrap::ExtrapToZHelix: Entering ------ "<<endl;
  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
  Double_t forwardBackward; // +1 if forward, -1 if backward
  if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 
  else forwardBackward = -1.0;
  Double_t v3[7], v3New[7]; // 7 in parameter ????
  Int_t i3, stepNumber;
  // For safety: return kTRUE or kFALSE ????
  // Parameter vector for calling EXTRAP_ONESTEP
  ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
  // sign of charge (sign of fInverseBendingMomentum if forward motion)
  // must be changed if backward extrapolation
  Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseTransverseMomentum());
//  cout<<"chargeExtrap = "<<chargeExtrap<<endl;

  // Extrapolation loop
  stepNumber = 0;
//  cout<<" (-forwardBackward * (v3[2] - zEnd)) = "<<(-forwardBackward * (v3[2] - zEnd))<<endl;
  while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
    stepNumber++;
    ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
//    cout<<" (-forwardBackward * (v3New[2] - zEnd)) = "<<(-forwardBackward * (v3New[2] - zEnd))<<endl;

    if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
                   // better use TArray ????
    for (i3 = 0; i3 < 7; i3++) {
//      cout<<" v3New["<<i3<< "] = "<<v3New[i3]<<endl;
      v3[i3] = v3New[i3];
    }
  }
  // check fgkMaxStepNumber ????
  // Interpolation back to exact Z (2nd order)
  // should be in function ???? using TArray ????
  Double_t dZ12 = v3New[2] - v3[2]; // 1->2
  if (TMath::Abs(dZ12) > 0) {
    Double_t dZ1i = zEnd - v3[2]; // 1-i
    Double_t dZi2 = v3New[2] - zEnd; // i->2
    Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
    Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
    Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
    Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
    v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
    v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
    v3[2] = zEnd; // Z
    Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
    Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
    // (PX, PY, PZ)/PTOT assuming forward motion
    v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
    v3[3] = xPrimeI * v3[5]; // PX/PTOT
    v3[4] = yPrimeI * v3[5]; // PY/PTOT
  } else {
    cout<<"W-AliMFTTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
  }
  // Recover track parameters (charge back for forward motion)
  RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
  return kTRUE;
}

//__________________________________________________________________________
Bool_t AliMFTTrackExtrap::ExtrapToZRungekutta(AliMFTTrackParam* trackParam, Double_t zEnd)
{
  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
  Double_t forwardBackward; // +1 if forward, -1 if backward
  if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
  else forwardBackward = -1.0;
  // sign of charge (sign of fInverseBendingMomentum if forward motion)
  // must be changed if backward extrapolation
  Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseTransverseMomentum());
  Double_t v3[7], v3New[7];
  Double_t dZ, step;
  Int_t stepNumber = 0;
  
  // Extrapolation loop (until within tolerance or the track turn around)
  Double_t residue = zEnd - trackParam->GetZ();
  Bool_t uturn = kFALSE;
  Bool_t trackingFailed = kFALSE;
  Bool_t tooManyStep = kFALSE;
  while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
    
    dZ = zEnd - trackParam->GetZ();
    // step lenght assuming linear trajectory
    step = dZ * TMath::Sqrt(1.0 + trackParam->GetSlopeY()*trackParam->GetSlopeY() +
                            trackParam->GetSlopeX()*trackParam->GetSlopeX());
    ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
    
    do { // reduce step lenght while zEnd oversteped
      if (stepNumber > fgkMaxStepNumber) {
        cout<<"W-AliMFTTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
        tooManyStep = kTRUE;
        break;
      }
      stepNumber ++;
      step = TMath::Abs(step);
      if (!AliMFTTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New)) {
        trackingFailed = kTRUE;
        break;
      }
      residue = zEnd - v3New[2];
      step *= dZ/(v3New[2]-trackParam->GetZ());
    } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
    
    if (trackingFailed) break;
    else if (v3New[5]*v3[5] < 0) { // the track turned around
      cout<<"W-AliMFTTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
      uturn = kTRUE;
      break;
    } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
    
  }
  
  // terminate the extropolation with a straight line up to the exact "zEnd" value
//  if (trackingFailed || uturn) {
//    
//    // track ends +-100 meters away in the bending direction
//    dZ = zEnd - v3[2];
//    Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
//    Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
//    Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
//    trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
//    trackParam->SetNonBendingSlope(nonBendingSlope);
//    trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
//    trackParam->SetBendingSlope(bendingSlope);
//    trackParam->SetZ(zEnd);
//    
//    return kFALSE;
//    
//  } else {
//    
//    // track extrapolated normally
//    trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
//    trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
//    trackParam->SetZ(zEnd);
//    
//    return !tooManyStep;
//    
//  }
  
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ConvertTrackParamForExtrap(AliMFTTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
{
  v3[0] = trackParam->GetX(); // X
  v3[1] = trackParam->GetY(); // Y
  v3[2] = trackParam->GetZ(); // Z
  Double_t slopeX = trackParam->GetSlopeX() ;
  Double_t slopeY = trackParam->GetSlopeY() ;
  Double_t slope2 = TMath::Sqrt(1.+slopeX*slopeX +slopeY*slopeY);
  Double_t pt = TMath::Abs(1.0 / trackParam->GetInverseTransverseMomentum());
  v3[6] = pt*slope2/TMath::Sqrt(slopeX*slopeX +slopeY*slopeY); // PTOT

  v3[5] = -forwardBackward / slope2; // PZ/PTOT spectro. z<0
  v3[3] = slopeX / slope2; // PX/PTOT
  v3[4] = slopeY / slope2; // PY/PTOT

  
//  v3[0] = trackParam->GetX(); // X
//  v3[1] = trackParam->GetY(); // Y
//  v3[2] = trackParam->GetZ(); // Z
//  Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseMomentum());
//  Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetSlopeY() * trackParam->GetSlopeY());
//  v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetSlopeX() * trackParam->GetSlopeX()); // PTOT
//  v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
//  v3[3] = trackParam->GetSlopeX() * v3[5]; // PX/PTOT
//  v3[4] = trackParam->GetSlopeY() * v3[5]; // PY/PTOT

}

//__________________________________________________________________________
void AliMFTTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMFTTrackParam* trackParam)
{
  trackParam->SetX(v3[0]); // X
  trackParam->SetY(v3[1]); // Y
  trackParam->SetZ(v3[2]); // Z
  Double_t pt = v3[6]*TMath::Sqrt(1. - v3[5]*v3[5]);
  trackParam->SetInverseTransverseMomentum(charge/pt);
  trackParam->SetSlopeY(v3[4]/v3[5]);
  trackParam->SetSlopeX(v3[3]/v3[5]);
//
//  trackParam->SetX(v3[0]); // X
//  trackParam->SetY(v3[1]); // Y
//  trackParam->SetZ(v3[2]); // Z
//  Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
//  trackParam->SetInverseMomentum(charge/pYZ);
//  trackParam->SetSlopeY(v3[4]/v3[5]);
//  trackParam->SetSlopeX(v3[3]/v3[5]);

}

//__________________________________________________________________________
Bool_t AliMFTTrackExtrap::ExtrapToZCov(AliMFTTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
{
  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
  
  if (!fgFieldON) { // linear extrapolation if no magnetic field
    AliMFTTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
    return kTRUE;
  }
  
  // No need to propagate the covariance matrix if it does not exist
  if (!trackParam->CovariancesExist()) {
    cout<<"W-AliMFTTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
    // Extrapolate track parameters to "zEnd"
    return ExtrapToZ(trackParam,zEnd);
  }
  
  // Save the actual track parameters
  AliMFTTrackParam trackParamSave(*trackParam);
  TMatrixD paramSave(trackParamSave.GetParameters());
  Double_t zBegin = trackParamSave.GetZ();

  // Get reference to the parameter covariance matrix
  const TMatrixD& kParamCov = trackParam->GetCovariances();
  
  // Extrapolate track parameters to "zEnd"
  // Do not update the covariance matrix if the extrapolation failed
  if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
  
  // Get reference to the extrapolated parameters
  const TMatrixD& extrapParam = trackParam->GetParameters();
  
  // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
  Bool_t extrapStatus = kTRUE;
  TMatrixD jacob(5,5);
  jacob.Zero();
  TMatrixD dParam(5,1);
  Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
  for (Int_t i=0; i<5; i++) {
    // Skip jacobian calculation for parameters with no associated error
    if (kParamCov(i,i) <= 0.) continue;
    
    // Small variation of parameter i only
    for (Int_t j=0; j<5; j++) {
      if (j==i) {
        dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
        dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
      } else dParam(j,0) = 0.;
    }
    // Set new parameters
    trackParamSave.SetParameters(paramSave);
    trackParamSave.AddParameters(dParam);
    trackParamSave.SetZ(zBegin);
    // Extrapolate new track parameters to "zEnd"
    if (!ExtrapToZ(&trackParamSave,zEnd)) {
      cout<<"W-AliMFTTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
      extrapStatus = kFALSE;
    }

    // Calculate the jacobian
    TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);

    jacobji *= 1. / dParam(i,0);
   jacob.SetSub(0,i,jacobji);
  }
  cout<<"jacob"<<endl;
  jacob.Print();

  // Extrapolate track parameter covariances to "zEnd"
  cout<<"Initial Cov MAtrix "<<endl;
  kParamCov.Print();
  TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
  TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
  cout<<"Extrapolated Cov MAtrix "<<endl;
  tmp2.Print();

  trackParam->SetCovariances(tmp2);
  // Update the propagator if required
  if (updatePropagator) trackParam->UpdatePropagator(jacob);

//  return extrapStatus;
  return kTRUE;
}

void AliMFTTrackExtrap::AddMCSEffectInAbsorber(AliMFTTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
{
//
//  // absorber related covariance parameters
//  Double_t bendingSlope = param->GetSlopeY();
//  Double_t nonBendingSlope = param->GetSlopeX();
//  Double_t inverseBendingMomentum = param->GetInverseMomentum();
//  Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
//                    (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
//  Double_t pathLength = TMath::Abs(signedPathLength);
//  Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
//  Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
//  Double_t varSlop = alpha2 * f0;
//  
//  // Set MCS covariance matrix
//  TMatrixD newParamCov(param->GetCovariances());
//  // Non bending plane
//  newParamCov(0,0) += varCoor;       newParamCov(0,1) += covCorrSlope;
//  newParamCov(1,0) += covCorrSlope;  newParamCov(1,1) += varSlop;
//  // Bending plane
//  newParamCov(2,2) += varCoor;       newParamCov(2,3) += covCorrSlope;
//  newParamCov(3,2) += covCorrSlope;  newParamCov(3,3) += varSlop;
//  
//  // Set momentum related covariances if B!=0
//  if (fgFieldON) {
//    // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
//    Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
//    Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
//                              (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
//    // Inverse bending momentum (due to dependences with bending and non bending slopes)
//    newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
//    newParamCov(4,1) += dqPxydSlopeX * varSlop;      newParamCov(1,4) += dqPxydSlopeX * varSlop;
//    newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
//    newParamCov(4,3) += dqPxydSlopeY * varSlop;      newParamCov(3,4) += dqPxydSlopeY * varSlop;
//    newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
//  }
//  
//  // Set new covariances
//  param->SetCovariances(newParamCov);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::CorrectMCSEffectInAbsorber(AliMFTTrackParam* param,
                Double_t xVtx, Double_t yVtx, Double_t zVtx,
                Double_t errXVtx, Double_t errYVtx,
                Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
{
//  /// Correct parameters and corresponding covariances using Branson correction
//  /// - input param are parameters and covariances at the end of absorber
//  /// - output param are parameters and covariances at vertex
//  /// Absorber correction parameters are supposed to be calculated at the current track z-position
//  
//  // Position of the Branson plane (spectro. (z<0))
//  Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
//  
//  // Add MCS effects to current parameter covariances (spectro. (z<0))
//  AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
//  
//  // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
//  ExtrapToZCov(param,zVtx);
//  LinearExtrapToZCov(param,zB);
//  
//  // compute track parameters at vertex
//  TMatrixD newParam(5,1);
//  newParam(0,0) = xVtx;
//  newParam(1,0) = (param->GetX() - xVtx) / (zB - zVtx);
//  newParam(2,0) = yVtx;
//  newParam(3,0) = (param->GetY() - yVtx) / (zB - zVtx);
//  newParam(4,0) = param->GetCharge() / param->P() *
//                  TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
//      TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
//  
//  // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
//  TMatrixD paramCovP(param->GetCovariances());
//  Cov2CovP(param->GetParameters(),paramCovP);
//  
//  // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
//  TMatrixD paramCovVtx(5,5);
//  paramCovVtx.Zero();
//  paramCovVtx(0,0) = errXVtx * errXVtx;
//  paramCovVtx(1,1) = paramCovP(0,0);
//  paramCovVtx(2,2) = errYVtx * errYVtx;
//  paramCovVtx(3,3) = paramCovP(2,2);
//  paramCovVtx(4,4) = paramCovP(4,4);
//  paramCovVtx(1,3) = paramCovP(0,2);
//  paramCovVtx(3,1) = paramCovP(2,0);
//  paramCovVtx(1,4) = paramCovP(0,4);
//  paramCovVtx(4,1) = paramCovP(4,0);
//  paramCovVtx(3,4) = paramCovP(2,4);
//  paramCovVtx(4,3) = paramCovP(4,2);
//  
//  // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
//  TMatrixD jacob(5,5);
//  jacob.UnitMatrix();
//  jacob(1,0) = - 1. / (zB - zVtx);
//  jacob(1,1) = 1. / (zB - zVtx);
//  jacob(3,2) = - 1. / (zB - zVtx);
//  jacob(3,3) = 1. / (zB - zVtx);
//  
//  // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
//  TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
//  TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
//  
//  // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
//  CovP2Cov(newParam,newParamCov);
//  
//  // Set parameters and covariances at vertex
//  param->SetParameters(newParam);
//  param->SetZ(zVtx);
//  param->SetCovariances(newParamCov);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::CorrectELossEffectInAbsorber(AliMFTTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
{
  
//  // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
//  TMatrixD newParamCov(param->GetCovariances());
//  Cov2CovP(param->GetParameters(),newParamCov);
//  
//  // Compute new parameters corrected for energy loss
//  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
//  Double_t p = param->P();
//  Double_t e = TMath::Sqrt(p*p + muMass*muMass);
//  Double_t eCorr = e + eLoss;
//  Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
//  Double_t nonBendingSlope = param->GetSlopeX();
//  Double_t bendingSlope = param->GetSlopeY();
//  param->SetInverseMomentum(param->GetCharge() / pCorr *
//           TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
//           TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
//  
//  // Add effects of energy loss fluctuation to covariances
//  newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
//  
//  // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
//  CovP2Cov(param->GetParameters(),newParamCov);
//  
//  // Set new parameter covariances
//  param->SetCovariances(newParamCov);
}

//__________________________________________________________________________
Bool_t AliMFTTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
                  Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
                  Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
{
  // pathLength: path length between trackXYZIn and trackXYZOut (cm)
  // f0:         0th moment of z calculated with the inverse radiation-length distribution
  // f1:         1st moment of z calculated with the inverse radiation-length distribution
  // f2:         2nd moment of z calculated with the inverse radiation-length distribution
  // meanRho:    average density of crossed material (g/cm3)
  // totalELoss: total energy loss in absorber
  
  // Reset absorber's parameters
  pathLength = 0.;
  f0 = 0.;
  f1 = 0.;
  f2 = 0.;
  meanRho = 0.;
  totalELoss = 0.;
  sigmaELoss2 = 0.;
  
  // Check whether the geometry is available
  if (!gGeoManager) {
    cout<<"E-AliMFTTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
    return kFALSE;
  }
  
  // Initialize starting point and direction
  pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
         (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
         (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
  if (pathLength < TGeoShape::Tolerance()) return kFALSE;
  Double_t b[3];
  b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
  b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
  b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
  TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
  if (!currentnode) {
    cout<<"E-AliMFTTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
    return kFALSE;
  }
  
  // loop over absorber slices and calculate absorber's parameters
  Double_t rho = 0.; // material density (g/cm3)
  Double_t x0 = 0.;  // radiation-length (cm-1)
  Double_t atomicA = 0.; // A of material
  Double_t atomicZ = 0.; // Z of material
  Double_t atomicZoverA = 0.; // Z/A of material
  Double_t localPathLength = 0;
  Double_t remainingPathLength = pathLength;
  Double_t sigmaELoss = 0.;
  Double_t zB = trackXYZIn[2];
  Double_t zE, dzB, dzE;
  do {
    // Get material properties
    TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
    rho = material->GetDensity();
    x0 = material->GetRadLen();
    atomicA = material->GetA();
    atomicZ = material->GetZ();
    if(material->IsMixture()){
      TGeoMixture * mixture = (TGeoMixture*)material;
      atomicZoverA = 0.;
      Double_t sum = 0.;
      for (Int_t iel=0;iel<mixture->GetNelements();iel++){
  sum  += mixture->GetWmixt()[iel];
  atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
      }
      atomicZoverA/=sum;
    }
    else atomicZoverA = atomicZ/atomicA;
    
    // Get path length within this material
    gGeoManager->FindNextBoundary(remainingPathLength);
    localPathLength = gGeoManager->GetStep() + 1.e-6;
    // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
    if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
    else {
      currentnode = gGeoManager->Step();
      if (!currentnode) {
        cout<<"E-AliMFTTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
  f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
  return kFALSE;
      }
      if (!gGeoManager->IsEntering()) {
        // make another small step to try to enter in new absorber slice
        gGeoManager->SetStep(0.001);
  currentnode = gGeoManager->Step();
  if (!gGeoManager->IsEntering() || !currentnode) {
          cout<<"E-AliMFTTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
    f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
    return kFALSE;
  }
        localPathLength += 0.001;
      }
    }
    
    // calculate absorber's parameters
    zE = b[2] * localPathLength + zB;
    dzB = zB - trackXYZIn[2];
    dzE = zE - trackXYZIn[2];
    f0 += localPathLength / x0;
    f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
    f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
    meanRho += localPathLength * rho;
    totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
    sigmaELoss += EnergyLossFluctuation(pTotal, localPathLength, rho, atomicZoverA);
    
    // prepare next step
    zB = zE;
    remainingPathLength -= localPathLength;
  } while (remainingPathLength > TGeoShape::Tolerance());
  
  meanRho /= pathLength;
  sigmaELoss2 = sigmaELoss*sigmaELoss;
  
  return kTRUE;
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::GetMCSAngle2(const AliMFTTrackParam& param, Double_t dZ, Double_t x0)
{
  return 0.;
//  Double_t bendingSlope = param.GetSlopeY();
//  Double_t nonBendingSlope = param.GetSlopeX();
//  Double_t inverseTotalMomentum2 = param.GetInverseMomentum() * param.GetInverseMomentum() *
//                                   (1.0 + bendingSlope * bendingSlope) /
//                                   (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); 
//  // Path length in the material
//  Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
//  // relativistic velocity
//  Double_t velo = 1.;
//  // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
//  Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
//  
//  return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
}



//__________________________________________________________________________
void AliMFTTrackExtrap::AddMCSEffect(AliMFTTrackParam *param, Double_t dZ, Double_t x0)
{
  Double_t slopeX = param->GetSlopeX();
  Double_t slopeY = param->GetSlopeY();
  Double_t slope2 = slopeX*slopeX+slopeY*slopeY;
  
  Double_t inversePt = TMath::Abs(param->GetInverseTransverseMomentum());

  Double_t inverseTotalMomentum2 = inversePt*inversePt / (1. + 1./slope2 );
  // Path length in the material
  Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + slope2);
  Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength * x0 /dZ) : TMath::Abs(signedPathLength);
  // relativistic velocity
  Double_t velo = 1.;
  // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
  Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
  theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
 
  Double_t varCoor  = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
  Double_t varSlop  = theta02;
  Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02/ 2. : 0.;
  
  cout<<Form("theta02=%e inverseTotalMomentum2=%e signedPathLength=%e pathLengthOverX0=%e   ",theta02,inverseTotalMomentum2,signedPathLength,pathLengthOverX0 )<<endl;

    cout<<Form("dz=%e x0=%e varCoor=%e  varSlop=%e  covCorrSlope=%e ",dZ,x0,varCoor,varSlop,covCorrSlope )<<endl;
  // Set MCS covariance matrix
  TMatrixD newParamCov(param->GetCovariances());
  cout<<"Covariance avant MCS"<<endl;
  newParamCov.Print();
  // Non bending plane
  newParamCov(0,0) += varCoor;       newParamCov(0,2) += covCorrSlope;
  newParamCov(2,0) += covCorrSlope;  newParamCov(2,2) += varSlop;
  // Bending plane
  newParamCov(1,1) += varCoor;       newParamCov(1,3) += covCorrSlope;
  newParamCov(3,1) += covCorrSlope;  newParamCov(3,3) += varSlop;
  
  cout<<"Covariance apres MCS"<<endl;
  newParamCov.Print();

//  // Set momentum related covariances if B!=0
//  if (fgFieldON) {
//    // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
//    Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
//    Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
//                              (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
//    // Inverse bending momentum (due to dependences with bending and non bending slopes)
//    newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
//    newParamCov(4,1) += dqPxydSlopeX * varSlop;      newParamCov(1,4) += dqPxydSlopeX * varSlop;
//    newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
//    newParamCov(4,3) += dqPxydSlopeY * varSlop;      newParamCov(3,4) += dqPxydSlopeY * varSlop;
//    newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
//  }
//  cout<<"Covariance apres"<<endl;
//  newParamCov.Print();

  // Set new covariances
  param->SetCovariances(newParamCov);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapToVertex(AliMFTTrackParam* trackParam,
          Double_t xVtx, Double_t yVtx, Double_t zVtx,
          Double_t errXVtx, Double_t errYVtx,
          Bool_t correctForMCS, Bool_t correctForEnergyLoss)
{
  
//  if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
//  
//  if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
//    cout<<"E-AliMFTTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
//        <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
//    return;
//  }
//  
//  // Check the vertex position relatively to the absorber
//  if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
//    cout<<"W-AliMFTTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
//        <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
//  } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
//    cout<<"W-AliMFTTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
//        <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
//    if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
//    else ExtrapToZ(trackParam,zVtx);
//    return;
//  }
//  
//  // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
//  if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
//    cout<<"W-AliMFTTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
//        <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
//    if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
//    else ExtrapToZ(trackParam,zVtx);
//    return;
//  } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
//    cout<<"W-AliMFTTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
//        <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
//  } else {
//    if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
//    else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
//  }
//  
//  // Get absorber correction parameters assuming linear propagation in absorber
//  Double_t trackXYZOut[3];
//  trackXYZOut[0] = trackParam->GetX();
//  trackXYZOut[1] = trackParam->GetY();
//  trackXYZOut[2] = trackParam->GetZ();
//  Double_t trackXYZIn[3];
//  if (correctForMCS) { // assume linear propagation until the vertex
//    trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
//    trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
//    trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
//  } else {
//    AliMFTTrackParam trackParamIn(*trackParam);
//    ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
//    trackXYZIn[0] = trackParamIn.GetX();
//    trackXYZIn[1] = trackParamIn.GetY();
//    trackXYZIn[2] = trackParamIn.GetZ();
//  }
//  Double_t pTot = trackParam->P();
//  Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
//  if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
//    cout<<"E-AliMFTTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
//    if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
//    else ExtrapToZ(trackParam,zVtx);
//    return;
//  }
//  
//  // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
//  if (correctForMCS) {
//    
//    if (correctForEnergyLoss) {
//      
//      // Correct for multiple scattering and energy loss
//      CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
//      CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
//         trackXYZIn[2], pathLength, f0, f1, f2);
//      CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
//      
//    } else {
//      
//      // Correct for multiple scattering
//      CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
//         trackXYZIn[2], pathLength, f0, f1, f2);
//    }
//    
//  } else {
//    
//    if (correctForEnergyLoss) {
//      
//      // Correct for energy loss add multiple scattering dispersion in covariance matrix
//      CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
//      AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
//      ExtrapToZCov(trackParam, trackXYZIn[2]);
//      CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
//      ExtrapToZCov(trackParam, zVtx);
//      
//    } else {
//      
//      // add multiple scattering dispersion in covariance matrix
//      AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
//      ExtrapToZCov(trackParam, zVtx);
//      
//    }
//    
//  }
  
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapToVertex(AliMFTTrackParam* trackParam,
          Double_t xVtx, Double_t yVtx, Double_t zVtx,
          Double_t errXVtx, Double_t errYVtx)
{
  ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapToVertexWithoutELoss(AliMFTTrackParam* trackParam,
                Double_t xVtx, Double_t yVtx, Double_t zVtx,
                Double_t errXVtx, Double_t errYVtx)
{
  ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapToVertexWithoutBranson(AliMFTTrackParam* trackParam, Double_t zVtx)
{
  ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapToVertexUncorrected(AliMFTTrackParam* trackParam, Double_t zVtx)
{
  ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::TotalMomentumEnergyLoss(AliMFTTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
{
  
  if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
  
  // Check whether the geometry is available
  if (!gGeoManager) {
    cout<<"E-AliMFTTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
    return 0.;
  }
  
  // Get encountered material correction parameters assuming linear propagation from vertex to the track position
  Double_t trackXYZOut[3];
  trackXYZOut[0] = trackParam->GetX();
  trackXYZOut[1] = trackParam->GetY();
  trackXYZOut[2] = trackParam->GetZ();
  Double_t trackXYZIn[3];
  trackXYZIn[0] = xVtx;
  trackXYZIn[1] = yVtx;
  trackXYZIn[2] = zVtx;
  Double_t pTot = trackParam->P();
  Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
  GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
  
  // total momentum corrected for energy loss
  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
  Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
  Double_t eCorr = e + totalELoss;
  Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
  
  return pTotCorr - pTot;
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
{
  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
  
  // mean exitation energy (GeV)
  Double_t i;
  if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
  else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
  
  return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
}

//__________________________________________________________________________
Double_t AliMFTTrackExtrap::EnergyLossFluctuation(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
{
  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
  //Double_t eMass = 0.510998918e-3; // GeV
  Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
  Double_t p2=pTotal*pTotal;
  Double_t beta2=p2/(p2 + muMass*muMass);
  
  Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
  Double_t sigma = fwhm / TMath::Sqrt(8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
  
  //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
  
  return sigma;
}

//__________________________________________________________________________
void AliMFTTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
{
  
  // charge * total momentum
  Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
                   TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
  
  // Jacobian of the opposite transformation
  TMatrixD jacob(5,5);
  jacob.UnitMatrix();
  jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
  jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
                 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
  jacob(4,4) = - qPTot / param(4,0);
  
  // compute covariances in new coordinate system
  TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
  cov.Mult(jacob,tmp);
}

//__________________________________________________________________________
void AliMFTTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
{
  
  // charge * total momentum
  Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
                   TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
  
  // Jacobian of the transformation
  TMatrixD jacob(5,5);
  jacob.UnitMatrix();
  jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
  jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
                 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
  jacob(4,4) = - param(4,0) / qPTot;
  
  // compute covariances in new coordinate system
  TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
  covP.Mult(jacob,tmp);
}

 //__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
{

// modif: everything in double precision

    Double_t xyz[3], h[4], hxp[3];
    Double_t h2xy, hp, rho, tet;
    Double_t sint, sintt, tsint, cos1t;
    Double_t f1, f2, f3, f4, f5, f6;

    const Int_t kix  = 0;
    const Int_t kiy  = 1;
    const Int_t kiz  = 2;
    const Int_t kipx = 3;
    const Int_t kipy = 4;
    const Int_t kipz = 5;
    const Int_t kipp = 6;
//  cout<<"vin  ="<< vect[kix]<<" "<< vect[kiy]<<" "<< vect[kiz]<<" pxyz/ptot "<< vect[kipx]<<" "<< vect[kipy]<<" "<< vect[kipz]<<endl;

    const Double_t kec = 2.9979251e-4;
    //
    //    ------------------------------------------------------------------
    //
    //       units are kgauss,centimeters,gev/c
    //
    vout[kipp] = vect[kipp];
    if (TMath::Abs(charge) < 0.00001) {
      for (Int_t i = 0; i < 3; i++) {
  vout[i] = vect[i] + step * vect[i+3];
  vout[i+3] = vect[i+3];
      }
      return;
    }
    xyz[0]    = vect[kix] + 0.5 * step * vect[kipx];
    xyz[1]    = vect[kiy] + 0.5 * step * vect[kipy];
    xyz[2]    = vect[kiz] + 0.5 * step * vect[kipz];

    //cmodif: call gufld (xyz, h) changed into:
    TGeoGlobalMagField::Instance()->Field(xyz,h);
    h2xy = h[0]*h[0] + h[1]*h[1];
    h[3] = h[2]*h[2]+ h2xy;
// cout<<"Field ="<< h[0]<<" "<< h[1]<<" "<< h[2]<<" "<< h[3]<<endl;
    if (h[3] < 1.e-12) {
      for (Int_t i = 0; i < 3; i++) {
  vout[i] = vect[i] + step * vect[i+3];
  vout[i+3] = vect[i+3];
      }
      return;
    }
    if (h2xy < 1.e-12*h[3]) {
      ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
      return;
    }
    h[3] = TMath::Sqrt(h[3]);
    h[0] /= h[3];
    h[1] /= h[3];
    h[2] /= h[3];
    h[3] *= kec;

    hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
    hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
    hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
 
    hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];

    rho = -charge*h[3]/vect[kipp];
    tet = rho * step;

    if (TMath::Abs(tet) > 0.15) {
      sint = TMath::Sin(tet);
      sintt = (sint/tet);
      tsint = (tet-sint)/tet;
      cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
    } else {
      tsint = tet*tet/36.;
      sintt = (1. - tsint);
      sint = tet*sintt;
      cos1t = 0.5*tet;
    }

    f1 = step * sintt;
    f2 = step * cos1t;
    f3 = step * tsint * hp;
    f4 = -tet*cos1t;
    f5 = sint;
    f6 = tet * cos1t * hp;
 
    vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
    vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
    vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
 
    vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
    vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
    vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
//    cout<<"vout ="<< vout[kix]<<" "<< vout[kiy]<<" "<< vout[kiz]<<" pxyz/ptot "<< vout[kipx]<<" "<< vout[kipy]<<" "<< vout[kipz]<<endl;
//  cout<<"vlin ="<< vect[kix] + step * vect[kix+3]<<" "<< vect[kiy] + step * vect[kiy+3]<<" "<< vect[kiz] + step * vect[kiz+3]<<" pxyz/ptot "<< vect[kipx]<<" "<< vect[kipy]<<" "<< vect[kipz]<<endl;


    return;
}

 //__________________________________________________________________________
void AliMFTTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
{

    Double_t hxp[3];
    Double_t h4, hp, rho, tet;
    Double_t sint, sintt, tsint, cos1t;
    Double_t f1, f2, f3, f4, f5, f6;

    const Int_t kix  = 0;
    const Int_t kiy  = 1;
    const Int_t kiz  = 2;
    const Int_t kipx = 3;
    const Int_t kipy = 4;
    const Int_t kipz = 5;
    const Int_t kipp = 6;

    const Double_t kec = 2.9979251e-4;

// 
//     ------------------------------------------------------------------
// 
//       units are kgauss,centimeters,gev/c
// 
    vout[kipp] = vect[kipp];
    h4 = field * kec;

    hxp[0] = - vect[kipy];
    hxp[1] = + vect[kipx];
 
    hp = vect[kipz];

    rho = -h4/vect[kipp];
    tet = rho * step;
    if (TMath::Abs(tet) > 0.15) {
      sint = TMath::Sin(tet);
      sintt = (sint/tet);
      tsint = (tet-sint)/tet;
      cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
    } else {
      tsint = tet*tet/36.;
      sintt = (1. - tsint);
      sint = tet*sintt;
      cos1t = 0.5*tet;
    }

    f1 = step * sintt;
    f2 = step * cos1t;
    f3 = step * tsint * hp;
    f4 = -tet*cos1t;
    f5 = sint;
    f6 = tet * cos1t * hp;
 
    vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
    vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
    vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
 
    vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
    vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
    vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;

    return;
}

 //__________________________________________________________________________
Bool_t AliMFTTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
{

    Double_t h2, h4, f[4];
    Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
    Double_t a, b, c, ph,ph2;
    Double_t secxs[4],secys[4],seczs[4],hxp[3];
    Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
    Double_t est, at, bt, ct, cba;
    Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
    
    Double_t x;
    Double_t y;
    Double_t z;
    
    Double_t xt;
    Double_t yt;
    Double_t zt;

    Double_t maxit = 1992;
    Double_t maxcut = 11;

    const Double_t kdlt   = 1e-4;
    const Double_t kdlt32 = kdlt/32.;
    const Double_t kthird = 1./3.;
    const Double_t khalf  = 0.5;
    const Double_t kec = 2.9979251e-4;

    const Double_t kpisqua = 9.86960440109;
    const Int_t kix  = 0;
    const Int_t kiy  = 1;
    const Int_t kiz  = 2;
    const Int_t kipx = 3;
    const Int_t kipy = 4;
    const Int_t kipz = 5;
  
    // *.
    // *.    ------------------------------------------------------------------
    // *.
    // *             this constant is for units cm,gev/c and kgauss
    // *
    Int_t iter = 0;
    Int_t ncut = 0;
    for(Int_t j = 0; j < 7; j++)
      vout[j] = vect[j];

    Double_t  pinv   = kec * charge / vect[6];
    Double_t tl = 0.;
    Double_t h = step;
    Double_t rest;

 
    do {
      rest  = step - tl;
      if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
      //cmodif: call gufld(vout,f) changed into:
      TGeoGlobalMagField::Instance()->Field(vout,f);

      // *
      // *             start of integration
      // *
      x      = vout[0];
      y      = vout[1];
      z      = vout[2];
      a      = vout[3];
      b      = vout[4];
      c      = vout[5];

      h2     = khalf * h;
      h4     = khalf * h2;
      ph     = pinv * h;
      ph2    = khalf * ph;
      secxs[0] = (b * f[2] - c * f[1]) * ph2;
      secys[0] = (c * f[0] - a * f[2]) * ph2;
      seczs[0] = (a * f[1] - b * f[0]) * ph2;
      ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
      if (ang2 > kpisqua) break;

      dxt    = h2 * a + h4 * secxs[0];
      dyt    = h2 * b + h4 * secys[0];
      dzt    = h2 * c + h4 * seczs[0];
      xt     = x + dxt;
      yt     = y + dyt;
      zt     = z + dzt;
      // *
      // *              second intermediate point
      // *

      est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
      if (est > h) {
  if (ncut++ > maxcut) break;
  h *= khalf;
  continue;
      }
 
      xyzt[0] = xt;
      xyzt[1] = yt;
      xyzt[2] = zt;

      //cmodif: call gufld(xyzt,f) changed into:
      TGeoGlobalMagField::Instance()->Field(xyzt,f);

      at     = a + secxs[0];
      bt     = b + secys[0];
      ct     = c + seczs[0];

      secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
      secys[1] = (ct * f[0] - at * f[2]) * ph2;
      seczs[1] = (at * f[1] - bt * f[0]) * ph2;
      at     = a + secxs[1];
      bt     = b + secys[1];
      ct     = c + seczs[1];
      secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
      secys[2] = (ct * f[0] - at * f[2]) * ph2;
      seczs[2] = (at * f[1] - bt * f[0]) * ph2;
      dxt    = h * (a + secxs[2]);
      dyt    = h * (b + secys[2]);
      dzt    = h * (c + seczs[2]);
      xt     = x + dxt;
      yt     = y + dyt;
      zt     = z + dzt;
      at     = a + 2.*secxs[2];
      bt     = b + 2.*secys[2];
      ct     = c + 2.*seczs[2];

      est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
      if (est > 2.*TMath::Abs(h)) {
  if (ncut++ > maxcut) break;
  h *= khalf;
  continue;
      }
 
      xyzt[0] = xt;
      xyzt[1] = yt;
      xyzt[2] = zt;

      //cmodif: call gufld(xyzt,f) changed into:
      TGeoGlobalMagField::Instance()->Field(xyzt,f);

      z      = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
      y      = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
      x      = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;

      secxs[3] = (bt*f[2] - ct*f[1])* ph2;
      secys[3] = (ct*f[0] - at*f[2])* ph2;
      seczs[3] = (at*f[1] - bt*f[0])* ph2;
      a      = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
      b      = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
      c      = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;

      est    = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
  + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
  + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));

      if (est > kdlt && TMath::Abs(h) > 1.e-4) {
  if (ncut++ > maxcut) break;
  h *= khalf;
  continue;
      }

      ncut = 0;
      // *               if too many iterations, go to helix
      if (iter++ > maxit) break;

      tl += h;
      if (est < kdlt32) 
  h *= 2.;
      cba    = 1./ TMath::Sqrt(a*a + b*b + c*c);
      vout[0] = x;
      vout[1] = y;
      vout[2] = z;
      vout[3] = cba*a;
      vout[4] = cba*b;
      vout[5] = cba*c;
      rest = step - tl;
      if (step < 0.) rest = -rest;
      if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;

    } while(1);

    // angle too big, use helix
    cout<<"W-AliMFTTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;

    f1  = f[0];
    f2  = f[1];
    f3  = f[2];
    f4  = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
    if (f4 < 1.e-10) {
      cout<<"E-AliMFTTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
      cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
      return kFALSE;
    }
    rho = -f4*pinv;
    tet = rho * step;
 
    hnorm = 1./f4;
    f1 = f1*hnorm;
    f2 = f2*hnorm;
    f3 = f3*hnorm;

    hxp[0] = f2*vect[kipz] - f3*vect[kipy];
    hxp[1] = f3*vect[kipx] - f1*vect[kipz];
    hxp[2] = f1*vect[kipy] - f2*vect[kipx];
 
    hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];

    rho1 = 1./rho;
    sint = TMath::Sin(tet);
    cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);

    g1 = sint*rho1;
    g2 = cost*rho1;
    g3 = (tet-sint) * hp*rho1;
    g4 = -cost;
    g5 = sint;
    g6 = cost * hp;
 
    vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
    vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
    vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
 
    vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
    vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
    vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;

    return kTRUE;
}